1. Field of the Invention
The present invention relates to continuous or discontinuous fibers or bars of optimized geometries for reinforcement of cement, ceramic, and polymeric based matrices. More specifically, the present invention relates to fibers of optimized geometries in which the ratio of lateral surface area available for bond per unit length of fiber to the cross-sectional area of the fiber, is larger than the corresponding ratio of a cylindrical fiber of same cross-sectional area.
2. Background Information
Cement and ceramic matrices are brittle in nature. They generally have a compressive strength much higher than their tensile strength. Thus, they tend to crack under tensile stresses. The addition of discontinuous fibers to the mixture has lead to improvements in numerous mechanical properties such as tensile and bending strength, energy absorption, toughness, etc.
Currently available fibers for cement based matrices can be classified according to the material of which they are made. Steel fibers can be found in different forms: round (cut from wire), flat (sheared from steel sheets), and irregularly shaped from melt. Their bond is generally enhanced by mechanical deformations such as crimping, adding hooks or paddles at their ends, or roughening their surface.
Glass and carbon fibers generally come in bundles or strands, each strand having a number of filaments. Polymeric fibers come in various forms including monofilament, fibrillated film network, bundles, twisted yams, braided strands as well as other forms. They may have a treated surface (etching or plasma treatment) to improve bond.
A continuous fiber or bar is defined as a fiber at least as long as the element or part of the element it is meant to reinforce; the term "continuous" may also refer to a fiber having a very high aspect ratio, defined as length over equivalent diameter. A bar can be made from a single fiber or a bundle of fibers. Of particular interest to this invention are fiber reinforced plastic (FRP) reinforcements in the form of bars for use in reinforced and prestressed concrete structures.
FRP reinforcements are essentially made from a bundle of strong stiff fibers embedded in a polymeric matrix such as an epoxy resin to form a bar-like reinforcing element. FRP reinforcements come in the form of bars, tendons, strands, and two or three dimensional meshes. FRP reinforcements utilizing high performance fibers such as carbon, glass, aramid (kevlar), and others, are seen primarily as a means to avoid corrosion problems otherwise encountered in concrete structures reinforced with conventional steel reinforcing bars or steel prestressing tendons. Their non-magnetic properties make them ideal for special applications such as radar stations and structures for magnetic levitation trains. Moreover, they can be beneficially used in structures subjected to certain chemicals and other harsh environments. However, one of the main drawbacks so far of FRP reinforcements has been their poor bond in comparison to conventional steel reinforcing bars or prestressing tendons.
As shown in FIG. 1, when a cementitous matrix reinforced with discontinuous fibers is subjected to a monotonic uniaxial load in tension, the following observations are generally made: 1) an initial almost linear response is observed (portion OA), followed by cracking; 2) the onset of cracking corresponds about to the deviation from linearity; 3) given the proper conditions (fiber and matrix reinforcing parameters) multiple cracking may occur (portion AB); 4) crack and damage localization follows stage 2 or 3; that is one main crack becomes critical and failure is imminent (point B); and 5) failure generally occurs by further opening of the critical crack (portion beyond B). When strong fibers are used, failure is generally characterized by fibers pulling out from the matrix. This implies that the bond between the fibers and the matrix essentially controls the maximum composite strength (point B of FIG. 1) that can be achieved. Furthermore, while it is desirable to utilize the strength of the fiber to the maximum extent possible, it is also desirable to allow the fibers to pull-out just before they break, in order to improve energy absorption and toughness. This bond failure is preferred, but at as high a value of stress as can possibly be achieved.
In current practice, where steel fibers are used with aspect ratios (length over diameter) of less than about 100, the average tensile stress induced in the fiber by bond at failure of the composite is only a fraction of the strength of the fiber. In analyzing the mechanics of fiber pull-out, the tensile stress in the fiber can be expressed in the following form: EQU .sigma..sub.t =P/A=(.SIGMA..sub.o L.sub.e .tau.)/A.ltoreq..sigma..sub.fu(1)
where:
P=applied pull-out load PA1 A=cross sectional area of the fiber PA1 .SIGMA..sub.o =external perimeter of cross section of fiber PA1 L.sub.e =embedded length of fiber PA1 .tau.=average bond strength at the fiber-matrix interface PA1 .sigma..sub.fu =tensile strength of the fiber
The above equation can be written in the following form: EQU .sigma..sub.t =(.SIGMA..sub.o /A)L.sub.e .tau. (2)
It can be observed that, for a given embedment length, L.sub.e, the fiber stress can be increased when either the bond strength, .tau., is increased, or the ratio (.SIGMA..sub.o /A) is increased, or both. For a round fiber of length L and diameter d, multiplying the ratio .SIGMA..sub.o /A by L/4 leads to L/d which is commonly referred to as the aspect ratio of the fiber, and is an important parameter in the mechanics of composites reinforced with discontinuous fibers.
The tensile stress, .sigma..sub.t (EQ. 2), can be increased by adding mechanical deformations to the fiber which increase the mechanical component of bond and thus improve the overall bond strength, .tau. In existing art, the mechanical component of bond is achieved, for example, by crimping or by providing hooks or paddles at the ends of the fibers. Crimping, while simple with metallic fibers, has the disadvantage of reducing the effective modulus of the fiber system; that is the effective modulus becomes smaller than the elastic modulus of the fiber material.
A very efficient method of improving the bond is by twisting the fiber. However, twisting is not always effective, such as: 1) twisting is not effective with round fibers, 2) twisting cannot be applied uniformly to fibers of irregular cross section, and 3) twisting leads to undesirable tunneling in fibers of flat cross-section; tunnel-like portions are difficult to penetrate by the matrix, leading to increased porosity, possible sites for stress concentration, and poorer interfacial zone between the fiber and the matrix. These effects tend to adversely affect the mechanical properties of the composite.
As shown above (EQ. 2), the tensile stress, .sigma..sub.t, in the fiber can also be increased by optimizing the geometry of the fiber such as by maximizing the external fiber perimeter for a given fiber cross-sectional area, that is .SIGMA..sub.o /A. Geometrically a round fiber has a minimum value of .SIGMA..sub.o /A when compared to other shapes of same cross section. Given a monofilament fiber material, one way to improve the ratio .SIGMA..sub.o /A is, for instance, to use a thin flat fiber. A flat fiber is defined here as a fiber of rectangular cross-section with the larger side being at least twice the smaller side.
However, it has been observed that a flat fiber does not mix with the cement matrix as well as a round fiber. The compactness of the fiber section and its stiffness in all directions, seems to influence the rheology of the mix and the performance of the resulting composite. This implies that for mixing purposes, a compact cross-section is better than a flat one.
EQUATION 2 can be rewritten in the following form: EQU .sigma..sub.t =(.SIGMA..sub.o 1/A)L.sub.e /l (3)
where l represents a unit length of fiber. Thus, the numerator of the ratio (.SIGMA..sub.o 1/A) represents the lateral area of the fiber per unit length, and the denominator represents its cross sectional area. It will be called here the Fiber Intrinsic Efficiency Ratio (FIER). For given bond conditions, maximizing the FIER should lead to maximizing the stress in the fiber and thus the composite strength prior to fiber pull-out. Thus: EQU FIER=(.SIGMA..sub.o .times.1)/A (4)
Accordingly, there is a need for an improved fiber for reinforcement of cement, ceramic, and polymeric based composites which provides a higher bond surface per unit cross-sectional area or per unit volume of fiber used. There is also a need for improved fibers for reinforcement of cement, ceramic, and polymeric based composites which can undergo mechanical deformations, particularly effective twisting along their longitudinal axis, to develop the mechanical component of bond and thus improve overall performance.
Finally, there is need for fibers of optimized geometry to improve the ascending portion of the pull-out load versus slip curve of the fiber, the maximum pull-out load of the fiber, the stress-strain response of the composite under various loadings, and the energy absorbing capacity of the composite.
For the case of continuous fibers or bars the optimized geometries developed in this invention allow for a higher lateral surface area for bond of a typical reinforcing bar, as well as possible twisting, or the execution of spiral-like deformations along the longitudinal axis of the bar, to improve the mechanical component of bond. These should lead to improvements in the composite wherever bond is important, such as in reducing average crack spacing, development length of bars in reinforced concrete, and transfer length of prestressed tendons. The increased lateral surface area of the new bar system developed makes it easier to grip the bar for tensioning in prestressed concrete applications.